Based on a complementary paradigm, the variational quantum eigensolver (VQE) algorithm is a hybrid quantum-classical algorithm, which
aims to find the lowest
eigenstate of the interacting many-body Hamiltonian by varying the energy expectation value function with respect to the parameters in the wavefunction ansätz [1]}, [2]}. The method relies upon the Rayleigh-Ritz variational principle [3]} and therefore provides an upper bound to the exact eigenenergy of the many-body Hamiltonian. It is worth adding at this point that the choice of a good ansätz can, in general, give results with excellent precision. One such widely used variational form is the chemically motivated unitary coupled cluster (UCC) ansätz. The coupled cluster approach, which is widely regarded as the gold standard of electronic structure calculations, is known to efficiently capture dynamical correlation in a system. However, in the regions of molecular strong correlation, which is attributed to the quasi-degeneracy of multiple constituent determinants, the traditional VQE algorithm may not fare well, and as a result, suffer from inconsistent description over the molecular potential energy surface (PES). On the other hand, the QPE algorithm does not possess the limitation if appropriate care taken to prepare the initial state, as we shall discuss next.
